Will I be able to restore a backup to the new mini even thought they have dissimilar OS's? I recall an issue with an iphone restore to a new iphone that would not let me proceed unless the OS's were the same.
Yes.
Migrating from your old Mac's Time Machine backup is the way to go.
see > Transfer to a new Mac with Migration Assistant - Apple Support
FWIW you will be Migrating from the Time Machine backup, not Restoring.
Indeed, surest approach is use of TM backup.
Personnally, (and if you feel comfortable with this) i would not be tempted to use a backup.
1) Have all data (documents, images, movies, desktop, etc.) copied to an external drive using same names.
2) reinstall OS
3) pick and select the apps you really mean to use
4) Recopy data in corresponding folders on the new mac.
It may be slightly longer, but 1) you will take the opportunity of a “clean install” to… clean-up. And 2) you will avoid bringing back potential problems.
Note that while it “looks” longer, the reality is you will probably have to spend time updating some of these apps to the newer OS. So, “more time” is questionnable.
Restoring backup from mac mini Catalina to M4 mac
